# basic commands for creating a matrix

m1 = matrix(data = seq(1:9), nrow = 3, ncol = 3, byrow = FALSE)

m1

m2 = matrix(data = c(1, 2, 3, 4, 5, 6, 7, 8, 9), nrow = 3, ncol = 3, byrow = TRUE)

m2

a = c(1, 2, 3)

b = c(4, 5, 6)

df = data.frame(a, b)

df

m3 = as.matrix(df)

m3

# basic ways to manipulate a matrix (transpose, inverse, multiplication)

m3.t = t(m3)

m3

m3.t

m4 = m3.t %*% m3

m4

m4.inv = solve(m4)

m4.inv

m5 = m4.inv %*% m4

m5

m6 = m5 %*% m4

m6

# load MLR.RData and MLRScript.R and examine

load("MLR.RData")

source("MLRScript.R")

head(metals)

pure

head(samples)

standards

# use absorbance values and concentrations for standards to predict eb

findeb(pure, standards)

eb

# use predicted eb values and absorbance values for samples to predict concentrations

findconc(samples, eb)

head(pred.conc)

# compare predicted and actual concentrations and evaluate error

diff = pred.conc - real.conc

head(diff)

help(apply)

means = apply(diff, 2, mean)

means

sds = apply(diff, 2, sd)

sds

conf.int = abs(qt(0.05/2, 23)) * sds

conf.int

diff$cobalt[abs(diff$cobalt) > conf.int[1]]

diff$nickel[abs(diff$nickel) > conf.int[2]]

diff$copper[abs(diff$copper) > conf.int[3]]

diff

# examine results for nickel

class(real.conc)

class(pred.conc)

predict = data.frame(pred.conc)

plot(real.conc$nickel, predict$nickel, pch = 19, col = "blue", xlab = "actual concentration of Ni", ylab = "predicted concentration of Ni" )

ni.lm = lm(predict$nickel ~ real.conc$nickel)

summary(ni.lm)

abline(ni.lm, col = "blue", lty = 2)

plot(real.conc$nickel, resid(ni.lm), pch = 19, col = "blue", ylim = c(-1.2e-3, 1.2e-3))

abline(h = means[2], col = "red", lty = 2)

abline(h = means[2] + conf.int[2], col = "red", lty = 2)

abline(h = means[2] - conf.int[2], col = "red", lty = 2)

identify(real.conc$nickel, resid(ni.lm), labels = c(2:7, 9:24, 26, 27))